You'll need an up-to-date version of Google Chrome to play the videos. You'll also need decent internet bandwidth to do streaming (2 MBit/s should be sufficient). If your internet accesss is too slow, you can always right click and download the video.

As far as the videos are concerned, Internet Explorer and Safari are not supported, because they do not understand the video format we're using.

And Chrome behaves much better than Firefox with the lecture video player, to the point of Firefox not even starting up properly. We're currently investigating. In the meantime, please use Chrome.

If you would still like to use Firefox and the page hangs (keeps displaying the spinny thing), pressing the "seek to start" button will usually return things to working order.

Description

This class will teach you how (and why!) integral equations let you solve many common types of partial differential equations robustly and quickly.

You will also see many fun numerical ideas and algorithms that bring these methods to life on a computer.

What to expect

A Gentle Intro: Linear Algebra/Numerics/Python warm-up

Some Potential Theory

The Laplace, Poisson, Helmholtz PDEs, and a few applications

Integral Equations for these and more PDEs

Ways to represent potentials

Quadrature, or: easy ways to compute difficult integrals

Tree codes and Fast Multipole Methods

Fun with the FFT

Linear algebra-based techniques ("Fast direct solvers"--if time)

What you should already know

You should have taken some sort of numerical analysis/numerical methods course.

There really aren't any books to cover our numerical and algorithmic needs.

So, unfortunately, there isn't one book that covers the entire class, or even a reasonable subset. It will occasionally be useful to refer to these books, but I would not recommend you go out and buy them just for this course. I will make sure they are available in the library for you to refer to.